Among various styles of tree drawing reported in the literature, balloon drawing enjoys a desirable feature of displaying tree structures in a rather balanced fashion. Each subtree in the balloon drawing of a tree is enclosed in a circle. Along any path from the root node, the radius of each circle reflects the number of descendants associated with the root node of the subtree. In this paper, w...

We consider the indirect covering subtree problem (Kim et al., 1996). The input is an edge weighted tree graph along with customers located at the nodes. Each customer is associated with a radius and a penalty. The goal is to locate a tree-shaped facility such that the sum of setup and penalty cost is minimized. The setup cost equals the sum of edge lengths taken by the facility and the penalty...

We improve the lower bound on the extremal version of the Maximum Agreement Subtree problem. Namely we prove that two binary trees on the same n leaves have subtrees with the same ≥ c log log n leaves which are homeomorphic, such that homeomorphism is identity on the leaves.

Consider a rooted tree with leaf-set and all nonleaf vertices having out-degree 2, at least. A is induced by in if the lowest common ancestor subtree for , its degree-2 suppressed. “maximum agreement subtree” (MAST) pair of two trees largest such that both . Bryant, McKenzie, Steel [BioConsensus, AMS, Providence, RI, 2003, pp. 55–65] Bernstein et al. [SIAM J. Discrete Math., 29 (2015), 2065–207...

A subtree of a tree is any induced subgraph that again (i.e., connected). The mean order the average number vertices its subtrees. This invariant was first analyzed in 1980s by Jamison. An intriguing open question raised Jamison asks whether maximum order, given tree, always attained some caterpillar. While we do not completely resolve this conjecture, find evidence favor proving different feat...

As a technology based on database, statistics and AI, data mining provides biological research a useful information analyzing tool. The key factors which influence the performance of biological data mining approaches are the large-scale of biological data and the high similarities among patterns mined. In this paper, we present an efficient algorithm named IRTM for mining frequent subtrees embe...

We study the number of subtrees on the fringe of random recursive trees and random binary search trees whose limit law is known to be either normal or Poisson or degenerate depending on the size of the subtree. We introduce a new approach to this problem which helps us to further clarify this phenomenon. More precisely, we derive optimal Berry-Esseen bounds and local limit theorems for the norm...

In this paper, we develop a new entropic matching kernel for weighted graphs by aligning depthbased representations. We demonstrate that this kernel can be seen as an aligned subtree kernel that incorporates explicit subtree correspondences, and thus addresses the drawback of neglecting the relative locations between substructures that arises in the R-convolution kernels. Experiments on standar...